Abstract-Obtaining accurate system models for verification is a hard and time consuming process, which is seen by industry as a hindrance to adopt otherwise powerful modeldriven development techniques and tools. In this paper we pursue an alternative approach where an accurate high-level model can be automatically constructed from observations of a given black-box embedded system. We adapt algorithms for learning finite probabilistic automata from observed system behaviors. We prove that in the limit of large sample sizes the learned model will be an accurate representation of the data-generating system. In particular, in the large sample limit, the learned model and the original system will define the same probabilities for linear temporal logic (LTL) properties. Thus, we can perform PLTL model-checking on the learned model to infer properties of the system. We perform experiments learning models from system observations at different levels of abstraction. The experimental results show the learned models provide very good approximations for relevant properties of the original system.

We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available Primula tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating and differentiating these circuits in time linear in their size. We report on experimental results showing successful compilation and efficient inference on relational Bayesian networks, whose Primula-generated propositional instances have thousands of variables, and whose jointrees have clusters with hundreds of variables.

. (2016). Learning deterministic probabilistic automata from a model checking perspective. Machine Learning, 105(2), 255-299. https://doi.org/10.1007/s10994-016-5565-9General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.? Users may download and print one copy of any publication from the public portal for the purpose of private study or research. ? You may not further distribute the material or use it for any profit-making activity or commercial gain ? You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access to the work immediately and investigate your claim. Abstract Probabilistic automata models play an important role in the formal design and analysis of hard-and software systems. In this area of applications, one is often interested in formal model-checking procedures for verifying critical system properties. Since adequate system models are often difficult to design manually, we are interested in learning models from observed system behaviors. To this end we adopt techniques for learning finite probabilistic automata, notably the Alergia algorithm. In this paper we show how to extend the basic algorithm to also learn automata models for both reactive and timed systems. A key question of our investigation is to what extent one can expect a learned model to be a good approximation for the kind of probabilistic properties one wants to verify by model checking. We establish theoretical convergence properties for the learning algorithm as well as for probability estimates of system properties expressed in linear time temporal logic and linear continuous stochastic logic. We empirically compare the learning algorithm with statistical model checking and demonstrate the feasibility of the approach for practical system verification.

Relational Bayesian networks are an extension of the method of probabilistic model construction by Bayesian networks. They de ne probability distributions on nite relational structures by conditioning the probability of a ground atom ra 1 ; : : : ; a n on rst-order properties of a 1 ; : : : ; a n that have been established by previous random decisions. In this paper we investigate from a nite model theory perspective the convergence p r operties of the distributions de ned in this manner. A subclass of relational Bayesian networks is identi ed that de ne distributions with convergence laws for rst-order properties.

No abstract